The Georgia and New York DMV's operate independently so your suspended New York license will not have any effect on your Georgia application. You should nevertheless pay any due fines to avoid a criminal record.
It is called the compact law. If you are suspended, revoked, or denied in one state, you are the same in all the rest! It was instituted to keep bad drivers from just going to another state, getting a license there and blowing off the reasons for the action in the other state